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Numbers (Classification) (F)

Classify numbers for GCSE Foundation. Identify integers, rationals, and irrationals, and see how they fit into number sets so you choose the right method.

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Fascinating Fact:

In a science lab, irrational numbers cannot be written as a simple fraction, so √2 and π have decimals that never end or repeat in a pattern.

In GCSE Maths, you categorise numbers into sets such as natural numbers, integers, rational, and irrational. Knowing each set helps you pick valid methods, check calculator outputs, and justify answers clearly.

Key Terms

Integer: A whole number, positive, negative, or zero (…, −2, −1, 0, 1, 2, …).
Rational number: A number that can be written as a fraction a/b with integers a, b ( b≠0), including terminating or recurring decimals.
Irrational number: A number that cannot be written as a simple fraction, with a non-terminating, non-recurring decimal (e.g., √2, π).

Frequently Asked Questions (Click to see answers)

What is the difference between rational and irrational numbers?

Rational numbers can be written as a fraction of integers and have terminating or recurring decimals. Irrational numbers cannot be written as such fractions and their decimals never terminate or recur.

Is 0 rational and is it an integer?

Yes. Zero is an integer, and it is rational because it can be written as 0/1. It fits inside both the integer set and the rational set.

How can I tell if a decimal is rational?

If the decimal ends (like 0.375) or repeats a pattern forever (like 0.333...), it is rational. If it never ends and never repeats, it is irrational.